Radiative relaxation time of quasinormal optical modes in small dielectric particles

Abstract

Radiative relaxation times of optical states in small dielectric particles of arbitrary shape are calculated in the quasistatic limit up to the second order of perturbation theory, assuming that the polarization distribution for the optical states is known. The concept of antisymmetrical optical states, previously developed for a system of discrete dipoles, is generalized for the case of a bulk dielectric particle. We use the integral form of Maxwell's equations to obtain a general expansion of solutions for the polarization function inside a particle in terms of eigenfunctions of the integral interaction operator. Then we calculate imaginary parts of corresponding eigenvalues, which determine the radiative relaxation times of optical excitations, treating the non-Hermitian part of the interaction operator as a perturbation. The imaginary parts of eigenvalues are expanded in terms of total multipole moments of corresponding eigenmodes. Particles with special properties of symmetry can possess polarization modes with very large radiative relaxation time. We also discuss the possibility of application of the eigenfunction decomposition to numerical calculations of optical cross-sections for some particles of non-spherical shape.